MV-algebras, multiple bets and subjective states

MV-algebras, multiple bets and subjective states

In this paper MV-algebras, the algebras of èukasiewicz in®nite-valued logics, are interpreted in a structure of bets, and a subjective interpretation of ®nitely additive measures on MV-algebras is given. Ó 2000 Elsevier Science Inc. All rights reserved.

Chapter XVII: States of MV-algebras

On States on MV-algebras and their Applications

1 Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK-814 73 Bratislava, Slovakia E-mail: [email protected] In the frames of quantum structures, states are a very important notion that model probability on an algebraic structure. Already G. Boole observed that to calculate probability of event of the structure M , it is important to know only which two events A and B we c...

MV-algebras with internal states and probabilistic fuzzy logics

In this paper we enlarge the language of MV-algebras by a unary operation r equationally described so as to preserve the basic properties of a state in its original meaning. The resulting class of algebras will be called MV-algebras with internal state (or SMV-algebras for short). After discussing some basic algebraic properties of SMV-algebras, we apply them to the study of the coherence probl...

MV* - Algebras

In this paper we make an algebraic study of the variety of M V * –algebras introduced by C. C.Chang as an algebraic counterpart for a logic with positive and negative truth values. We build the algebraic theory of M V * –algebras within its own limits using a concept of ideal and of prime ideal that are very naturally related to the corresponding concepts in –groups. The main results are a subd...